This past Saturday we held our first QED (Chicago’s Youth Math Research Symposium) Brainstorming sessions at Payton. I worked with kids and parents to come up with as many math research questions as possible in 45 minutes. Some results:
- Ten people have a secret. These people gossip in pairs, and can share up to 3 secrets when such a pairing occurs. If they meet at random, what’s the probability that everyone will know all of the secrets after 30 meetings?
- How many 10 digit palindromes are divisible by 11?
- A 3×3 grid is made of toothpicks, and each toothpick has a color. How many colors do you need if 2 toothpicks can’t share the same color if they touch?
- There are slots to place numbers at the vertices of a cube, and at the midpoint of each edge. If each slot is filled with a number from 1 to 20, and each number is used only once, can you make the sum of the numbers on each face of the cube be the same? If so, in how many ways can you do it?
- Consider a triangle’s vertices and its midpoints (like the previous problem); there are multiple ways to place the numbers 1 to 6 in these ‘slots’ to make each side of the triangle have the same sum. Add a triangle by adjoining two more sides (and thus 3 more slots); repeat the puzzle with this figure, using the numbers 1 to 9. If you get that, keep adding to your row of triangles and repeat!
Everyone that attended found it liberating to spend our time just posing questions. Sign up and join us next weekend at math circles next weekend at UChicago to try it out! And if you can’t make it, the problems above are fair game for a QED project; everyone at Payton kept their favorites–these are the leftovers. 🙂